A provocative claim that Australian businesses struggle to recruit because of a “job snobs” problem that cited a survey of 14,000 employers was based on the views of only 29 companies, documents reveal.

Reports emerged in August that firms were having trouble hiring staff after the employment minister, Michaelia Cash, released the employment department’s annual employers’ recruitment insights paper.

The 2018 survey asked 14,000 companies across Australia about their recruitment process. A question asking whether employers had found their last recruitment round difficult had a sample size of 10,220; 45% said they had experienced difficulty, an increase from 2017.

First reported in the Australian newspaper, which said in a front page headline that “job snobs ‘are leaving bosses in the lurch’ ”, the annual report prompted further news coverage and debate about whether Australia has a “job snobs” problem.

The newspaper reported: “Employment minister Michaelia Cash said the research, which involved interviews with almost 14,000 employers across the nat­ion, showed ‘there are jobs out there for those who want them’ and her aim was to get ‘every Australian who is willing and able into a job.’ ”

But documents released to Labor under freedom of information show that although the overall survey quizzed 14,000 businesses, questions about a “lack of interest” from jobseekers were derived from qualitative research.

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The documents reveal there was a sample size of 29 employers for data showing the proportion of companies who cited applicants “lacking interest or employability skills” as a reason for their difficulty recruiting staff. Those data tables were presented together in the report.

Of those, 62% reported concerns about applicants “lacking interest or employability skills” and 38% did not.

Labor’s employment spokesman, Brendan O’Connor, said: “This is more damning evidence that minister Cash continues to mislead, misrepresent and misuse data about Australians trying to get a job.”

Overall the 52 businesses who took part in the qualitative research all had said they had experienced difficulty recruiting. They were based in Sydney, the Gold Coast and the Wimmera Mallee region.

The report published on the department’s website said employers were most likely to cite a lack of qualified or experienced applicants, candidates lacking interest in the position, and jobseekers not having the required skills. Others said applicants were not interested in the occupation or work conditions.

The data tables also said that of the 52 employers, 67% cited a lack of skills or qualifications as the reason for their difficulty employing people.

Cash did not use use the term “job snobs”. She told the Australian at the time: “We have an economy of opportunity and employers are screaming out for workers who are eager for a job. The dignity, value and importance of providing for yourself and your family cannot be understated.”

But the government has been accused of demonising jobseekers as it faces pressure on the low rate of the Newstart payment. It has previously released data to selected media outlets to suggest people were not taking their job search obligations seriously.

The data, analysed by Guardian Australia, shows more than 120,000 of those penalised under the Jobactive system were found to have a valid reason for not meeting their obligations.

In a recent change, the government has stopped providing detailed information in its official reports about the penalties imposed on vulnerable jobseekers, such as people who are experiencing homelessness, have a disability or mental health issues.